In the 1990s, she was posted in the NHS administrative system, taking up the position of chief executive of the Regional Health Authority of Oxford. In 1994, she was promoted to the position of NHS regional director for Anglia and Oxfordshire.[5] There were eight NHS regional directors in total after a re-organization that, by April 1996, abolished six management outposts and fourteen regional health-authorities.[5]

In late 2000, Stocking applied for the NHS top position.[7] In October 2000,
Nigel Crisp was nominated Chief Executive of the NHS, and Stocking director of the NHS Modernisation Agency, the body tasked with rolling out the NHS reforms.[8] In December 2000, she announced she would leave the public sector to join non-governmental, charity organizationOxfam.

Stocking, during her tenure, built Oxfam's relationships with major, international, private corporations such as Unilever, Monsoon, Sysco, and others, on "many diverse projects,"[10] while also Oxfam grew to become one of Britain's biggest retailers with more than 700 shops and, through its secondhand book outlets, the charity stood among Europe's biggest book retailers. In 2009, Oxfam's shops made a profit of about £20m on £80m of revenue, with the charity posting a record total revenue of £318m.

In a 2010 interview, she stated: "Times have changed, and Oxfam is moving with the times. It took a while for many in the organisation to understand what is happening but since the late 1990s we have seen quite different relationships develop with private business."[10]

In 2011, Oxfam launched a campaign for "food justice in a resource-constrained world." Stocking stated that the organization's focus would be also on helping small land-holders and nomadic tribes to establish their land rights against richer nations "such as China and the Gulf States gobbling up land in Africa."[10]

In February 2018, an investigation by the Times reported that, during Stocking's tenure, Oxfam allowed three men to resign and sacked four others for "gross misconduct" after an inquiry concerning sexual exploitation, the downloading of pornography, bullying, and intimidation by Oxfam's staff in Haiti.[12] The Times stated that an internal, confidential report was produced by Oxfam in 2011. It found that there had been “a culture of impunity” among some staff in Haiti and concluded that "it cannot be ruled out that any of the prostitutes were under-aged."[12] Among the staff who were permitted by Oxfam's leadership to resign without further actions taken against them was the charity's country director, Roland van Hauwermeiren. According to Oxfam's internal report, van Hauwermeiren admitted using prostitutes at a villa whose rent was paid with Oxfam funds means for charity. Stocking, Oxfam's CEO at the time, offered Hauwermeiren “a phased and dignified exit” invoking her concern that sacking him risked “potentially serious implications for the charity’s work and reputation."[13]

When the allegations became public in 2018, Stocking stated that her biggest work mistake had been “Not getting rid of people soon enough."[14] Murray Edwards College issued a statement disputing the allegation that Stocking was involved in a "cover up" and affirming that she has the "College’s full support".[15] Stocking postponed a planned February 2018 visit to the Cambridge Union in light of the 'considerable media attention' surrounding her involvement with Oxfam.[16]

Following the resignation of Penny Lawrence, Oxfam's deputy chief executive, Robert Halfon, ConservativeMP and Chairman of the Education Select Committee, accused Stocking of trying to “escape responsibility for the Haiti prostitution scandal." Halfon criticized the former Oxfam head who, he stated, had behaved “outrageously” in allowing senior aid workers to "resign quietly from the charity."[17]

In October 2017, Stocking announced that Murray Edwards would be changing its admissions policy to allow it to accept transgender students who identify as female. Stocking stated that the college is "open to all outstanding young women" and "so it is absolutely right, both legally and within [the college's] set of values, for anyone who identifies as female to be able to apply to study [in it]."[19]

In March 2015, Stocking was appointed Chair of an Independent Panel to assess the World Health Organization's response in the Ebola outbreak.[21] In 2016, she was appointed Chair of Trustees of the independent charity organization, A Blueprint for Better Business.[22]